Suppose that a risk averse individual has $1, and there are three assets; one safe, and two risky. The safe one yields a sure rate of return of 1. The risky ones have distribution functions F(y1) and F(y2) where assets have independent and identical distributions. Show that both risky assets have the same share in the optimal portfolio.
The optimal portfolio is a linear combination of the risk free asset and optimal risky portfolio. So to prove that both the risky portfolios have same share in optimal portfolio, we need to prove that the optimum risky portfolio will have the same proportion of two risky assets.
Let w1 and w2 are the proportion of two risky assets in optimum risky ...
The optimal portfolio is examined.